How to calc matrix4 that covert a set of point from one 3D coordinate to another 3D coordinate-CodePudding

Now n points(p1~pn) are given in a cartesian 3D coordinate system: L1. Actually, L1 is a local coordinate system of a 3D model.

And n points(P1~Pn) are given in the other cartesian 3D coordinate system: L2. L2 is the Earth-centered, Earth-fixed coordinate system: ECEF.

Pi represents the converted point of pi from L1 to L2.

Now I want to find the matrix4 that convert points in L1 to L2 with the minimum error. Is this possible mathematically? Any idea or suggestion would be thankful.

CodePudding user response：

There is a well known solution indeed. Look at the Kabsch algorithm:

https://en.m.wikipedia.org/wiki/Kabsch_algorithm

There are many packages implementing it out there.